A hydrostatic pressure test is used to assess the integrity of a vessel, such as a pipe. The vessel can, for example, be a section of a pipeline that has been cut from the remainder of the pipeline or a pipe that is to be added to a pipeline. The pipe is capped at both ends and filled with liquid pressurizing media. During the test, a pump incrementally forces an additional volume of media into the pipe with each stroke of the pump's piston. The pipe's internal pressure is monitored and provides an indication of a leak or other indication of lack of pipe integrity.